Autor:	Ardentov, A., Donne, E. Le, Sachkov, Yu.
Rok vydání:	2018
Předmět:	Mathematics - Differential Geometry Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces. Comment: 26 pages, 47 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.05431 Zobrazit plný text záznamu View this record from Arxiv